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Describe the Brief explanation of k-means and clustering.

Data Collection and Preprocessing

This report presents the findings from the analysis of the health and population data of Papua New Guinea. The analysis will cover the period from the year 2000 to the year 2015. The analysis aims at observing and identifying trends and relationships that may exist in the data and presenting findings that can be of value for other professionals.

The data used for the analysis in this report was obtained from the World Bank as Health and Population.csv. The data was then preprocessed to focus on the specific datasets on Papua New Guinea. The new data was then filtered to remain with six variables; Birth Rate, Death Rate, Unemployment Rate, Fertility Rate, Government Health Expenditure and Life Expectancy at Birth. The analysis involved three single variable analysis, two 2- variable analysis, a cluster analysis using k-means clustering and two linear regressions.

The findings presented from the analysis in this report focus mainly on Papua New Guinea and thus can only be considered as relevant for the country and cannot be used as reference for other countries. Although there could be an exception for countries with similar characteristics such as population size, income level and geographical location.

Secondary data was used for this report. The analyzed data was obtained from the World Bank as Health and Population.csv. Using excel the data was filtered to obtain the data on Papua New Guinea based on the six variables; Birth Rate, Death Rate, Unemployment Rate, Fertility Rate, Government Health Expenditure and Life Expectancy at Birth.

The new data is then imported into R using the code below:

#Importing the Papua New Guinea data into R as PNGData

PNGData <- read.csv("C:/Users/user/Documents/HNP WB DATA/PNGSpecifiedData.csv", header = T)

PNGData <- PNGData[,c(3,45:60)]

PNGData

To cater for the missing values, the analysis focused on the data from the years 2000 to the year 2015. This ensured a complete and continuous dataset that will be sufficient for providing reliable analysis.

The following code transposed the data to convert the variables into columns from rows:

#Intializing the Year, Birth Rate, Death Rate, Govt Health Expenditure, Fertility Rate,

#Life Expectancyat Birth and Unemployment as vectors

Year <- c(2000:2015)

Birth.Rate <- c(PNGData[1,])

Death.Rate <- c(PNGData[2,])

Govt.Health.Expenditure <- c(PNGData[3,])

Fertility.Rate <- c(PNGData[4,])

Life.Expectancy.At.Birth <- c(PNGData[5,])

Unemployment <- c (PNGData[6,]) 

#Forming a matrix for the initialized vectors of variables

PNGData1 <- matrix(c(Year,Birth.Rate,Death.Rate,Govt.Health.Expenditure,Fertility.Rate,

                     Life.Expectancy.At.Birth,Unemployment), ncol = 7, byrow = F)

#Naming the columns for the matrix

Analysis of Papua New Guinea Data

colnames(PNGData1) <- c("Year", "Birth.Rate","Death.Rate","Govt.Health.Expenditure",

                        "Fertility.Rate","Life.Expectancy.At.Birth","Unemployment")

#Forming the data frame for the matrix

PNGData1 <- data.frame(PNGData1)

PNGData1 <- PNGData1[c(1:16),]

PNGData1

This was achieved through first initializing all the variables as vectors i.e. converting all the rows in the PNGData into vectors. These vectors then formed the columns of a matrix, which is converted into a data frame to form the PNGData1 dataset.

The resultant data, PNGData is now in a format that can be analyzed.

  1. Exploratory Data Analsis
    • Single Variable Analysis
  2. Birth Rate

The analysis of the Birth Rate in Papua New Guinea from the years 2000 through to the year 2015 produced the plot below in figure 1. The R Code used to generate the plot is given below:

#Plotting the Birth Rate in Papua New Guinea

plot(PNGData1$Year, PNGData1$Birth.Rate, xlab = "Year", ylab = "Birth Rate", type = 'l',

     main = "Birth Rate of Papua New Guinea (2000 - 2015)" )

  1. Death Rate

The analysis of the Death Rate in Papua New Guinea from the years 2000 through to the year 2015 produced the plot below in figure 2. The R Code used to generate the plot is given below:

#Plotting the Death Rate in Papua New Guinea

plot(PNGData1$Year, PNGData1$Death.Rate, xlab = "Year", ylab = "Death Rate", type = 'l',

     main = "Death Rate in Papua New Guinea (2000 - 2015)")

The resultant plot is as below:  

  1. Unemployment

The analysis of the unemployment in Papua New Guinea from the years 2000 through to the year 2015 produced the plot below in figure 3. The R Code used to generate the plot is given below:

#Plotting the Unemployment in Papua New Guinea

plot(PNGData1$Year, PNGData1$Unemployment, xlab = "Year", ylab = "Unemployment", type = 'l',

     main = "Unemployment in Papua New Guinea (2000 - 2015)")

we observe that the unemployment rate in Papua New Guinea does not have a definable trend. The unemployment rate was on a decline between the years 2000 and 2010. It then spiked from 2010 to 2011 before relatively flattening out between 2011 and 2015.

  • Two Variable Analysis
  1. Birth Rate and Fertility Rate

The analysis of the relationship between the Birth Rate and the Death Rate in Papua New Guinea produced the plot in figure 4 below. The R Code used to generate the plot is as given below:

Plotting the Birth Rate against the Death Rate

plot(PNGData1$Birth.Rate, PNGData1$Fertility.Rate, xlab = "Fertility Rate", ylab = "Birth Rate",

     type = 'l', main = "Birth Rate against the Death Rate (2000 - 2015)")

The resultant plot is as below:

The plot indicates a direct linear relationship between the birth rate and the fertility rate in Papua New Guinea. This suggests that and increase in the fertility rate results in the increase in birth rate in Papua New Guinea.

  1. Death Rate and Health Expenditure

Linear Regression

The analysis of the relationship between the Death Rate and the Government Health Expenditure in Papua New Guinea produced the plot in figure 5 below. The R Code used to generate the plot is as given below:

#Plotting the Death Rate against the Government Health Expenditure

plot(PNGData1$Govt.Health.Expenditure, PNGData1$Death.Rate, xlab = "Govt Health Expenditure",

     ylab = "Death Rate", main = "Death Rate against the Government Health Expenditure (2000 - 2015)")

The plot in figure 5 above does not indicate any real linear relationship between the Government Health Expenditure and the Death Rate in Papua New Guinea. However, the plot does show a decrease in the death rate with increase in the Government Health Expenditure. Thus, implying that an increased investment in the Health Expenditure would be a good way of eventually reducing the death rate in Papua New Guinea.

  1. Advanced Analysis

Advanced analysis was carried out through clustering of the Papua New Guinea Dataset. The clustering was done using the k-means method.

The R Code used to generate the clusters is as given below:

#Clustering the Papua New Guinea data

#Loading The Cluster Package

library(cluster)

set.seed(20)

Clusters <- kmeans(PNGData1[2:3,],5)

Clusters

#Plotting the Clusters

clusplot(PNGData1, Clusters$cluster, color=T, shade=T,

         labels=2, lines=0)

The code above separated the periods 2000 to 2015 into 5 clusters. Table 1 below represents the output of the clustering of the Papua New Guinea Dataset:

K-means clustering with 5 clusters of sizes 3, 3, 4, 3, 3

Cluster means:

  Birth.Rate Death.Rate

1   29.50433   7.236667

2   30.83967   7.394333

3   33.45100   8.125000

4   32.11200   7.684333

5   28.29500   7.155333

Clustering vector:

 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16

 3  3  3  3  4  4  4  2  2  2  1  1  1  5  5  5

Within cluster sum of squares by cluster:

[1] 0.3808153 0.4070613 0.7141440 0.3530327 0.2697787

 (between_SS / total_SS =  96.5 %)

Available components:

[1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss" "betweenss"   

[7] "size"         "iter"         "ifault"

Table 1

From the plot above we observe that one of the clusters, cluster 1 above is bigger that the other 4.

  1. Linear Regression

Linear regression is described by (Faraway, 2006) as y=Xβ+ε, the relationship between an independent variable X and a dependent variable y.

In this report, we analyze the relationship between two pairs of variables as in below:

  1. Linear Model for Fertility Rate on Birth Rate

The R Code used for generating the linear model for Fertility Rate on Birth Rate is as below:

#Unlisting the Birth Rate and Fertility Rate data variables and storing in ModelData1

Clustering of Papua New Guinea Data

Model1Data <- data.frame(BirthRate = unlist(PNGData1$Birth.Rate),

                         FertilityRate = unlist(PNGData1$Fertility.Rate))

#Generating the linear model for Fertility Rate on Birth Rate

Model1 <- lm(BirthRate ~ FertilityRate, data = Model1Data)

Model1

#Plotting Model1 and its variables

plot(Model1) 

The data variables, Fertility Rate and Birth Rate are first unlisted to enable modelling.

The resultant output of the linear regression model is given in table 1 below:

Call:

lm(formula = BirthRate ~ FertilityRate, data = Model1Data)

Coefficients:

  (Intercept)  FertilityRate  

     -0.02953        7.53036

Table 2

From table 1 above, we can conclude that the linear model is given by:

BirthRate = -0.02953 + 7.53036FertilityRate

The model implies that the Fertility Rate has a positive impact on the Birth Rate, thus positive correlation. This is observed from the positive coefficient of the Fertility Rate = 7.53036.

The model also implies that at Fertility Rate = 0, the Birth Rate stands at -0.02953.

Linear Model for Govt Health Expenditure on Life Expectancy At Birth

The R Code used for generating the linear model for Fertility Rate on Birth Rate is as below:

#Unlisting the Life Expectancy At Birth and Govt Health Expenditure data variables and

#storing in ModelData2

Model2Data <- data.frame(LifeExpectancyAtBirth = unlist(PNGData1$Life.Expectancy.At.Birth),

                         GovtHealthExpenditure = unlist(PNGData1$Govt.Health.Expenditure))

#Generating the linear model for Govt Health Expenditure on Life Expectancy At Birth

Model2 <- lm(LifeExpectancyAtBirth ~ GovtHealthExpenditure, data = Model2Data)

Model2

#Plotting Model2 and its variables

plot(Model2)

The data variables, Government Health Expenditure and Life Expectancy At Birth are first unlisted to enable modelling.

The resultant output of the linear regression model is given in table 2 below:

Call:

lm(formula = LifeExpectancyAtBirth ~ GovtHealthExpenditure, data = Model2Data)

Coefficients:

          (Intercept)  GovtHealthExpenditure  

             61.75394                0.04434

Table 3

From table 2 above, we can conclude that the linear model is given by:

Life Expectancy At Birth = 0.04434 + 61.75394Government Health Expenditure

The model implies that the Government Health Expenditure has a positive impact on the Life Expectancy At Birth, thus positive correlation. This is observed from the positive coefficient of the Government Health Expenditure = 61.75394

The model also implies that at Government Health Expenditure = 0, the Life Expectancy at Birth stands at 0.04434.

The resultant Normal Q-Q plot is given in the figure 7 below:

References

Faraway, J. J. (2006). Extending The Linear Model with R (1st ed.). New York: Chapman & Hall/CRC.

Galit, S., Peter, B. C., Inbal, Y., & Nitin, P. R. (2018). Data Mining for Business Analytics (1st ed.). John Wiley & Sons, Inc.

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[Accessed 18 July 2024].

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My Assignment Help. Essay: Analysis Of Health And Population Data In Papua New Guinea. [Internet]. My Assignment Help. 2020 [cited 18 July 2024]. Available from: https://myassignmenthelp.com/free-samples/ict110-introduction-to-data-science/health-expenditure.html.

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